Monday March 14th at 4.30pm

that the membership and emptiness problem of relations constructed from finite relations with these operators and $\cup$ is decidable.

This generalizes Presburger arithmetics and allows to decide the reachability problem for those Petri nets where inhibitor arcs occur only

in some restricted way. Especially the reachability problem is decidable for Petri nets with only one inhibitor arc, which solves an open problem

in [KLM89]. Furthermore we describe the corresponding automaton having a decidable emptiness problem.